1 December 2006

Garrett Odell

Center for Cell Dynamics

University of Washington

Five years ago we (George von Dassow, Ed Munro, Eli Meir, and I - references below) made mathematical/computer models of two ancient, famous, genetic networks that act early in diverse embryos to establish spatial gene expression patterns prefiguring the body plan. Our models revealed these networks to be robust in the sense that they can continue to make the correct spatial pattern in the face of thousand-fold variations in the strengths and functional forms of interactions among participating genes and their products. Initially it surprised me that it was even possible to design networks with such properties, but I now believe only networks having this kind of robustness can be functionally heritable in polymorphic populations. How, other than by natural selection, could genetic networks acquire the kind of robustness I believe they must have even to enter the natural selection races?

To probe for answers, I wrote a computer program that haphazardly generates randomly connected networks made from about the same number of biochemically sensible parts that constitute the segment polarity and neurogenic networks. We (Harvard's own Bjorn Millard, Ed Munro, and I) devised computer algorithms that discover and catalog the stable expression patterns any network can make, and, from all these, distills those patterns the network can make robustly with respect to variations of its parameters. It turned out that 19 out of 20 random networks our program created could make at least one, and usually many, complex stable spatial expression patterns with the same high, or higher, robustness that the real, evolved, segment-polarity and neurogenic networks exhibit. Only 1 out of our 20 random networks was a complete loser; it could not make, robustly, any interesting pattern at all.

This result is repugnant to mathematicians and engineers - that, in some sense, the values of parameters do not matter - that biologists, who have seemed to be procrastinating forever about measuring parameter values (rate constants, half-lives, etc.), were instead presciently ignoring tedious and meaningless chores. What I want chiefly to focus on is a vision of what features of parameters and their range of values actually matter.

By the way, our algorithms for finding patterns any network can stabilize show that it's possible to replace the network's differential equation model, which keeps track of continuous concentrations of gene products changing continously through time, by discrete logic models with quantized far-apart concentrations. Unfortunately, there are many different ways to do this -- different ways for different parameter values, no way appropriate for all parameter values.

G von Dassow, E Meir, E M Munro, G M Odell, *"The segment polarity network is a robust developmental module"*, Nature 406:188-92 2000. PubMed

E Meir, G von Dassow, E M Munro, G M Odell, *"Robustness, flexibility, and the role of lateral inhibition in the neurogenic network"*, Current Biology 12:778-86 2002. PubMed